Research on the algebraic structure of theToda type non-autonomous discrete integrable systems and its applications

户田型非自治离散可积系统的代数结构及其应用研究

• 批准号: 18540214
• 负责人: TSUJIMOTO Satoshi
• 金额: $ 2.64万
• 依托单位: Kyoto University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2006
• 资助国家: 日本
• 起止时间: 2006 至 2009
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-18540214/
• 关键词: アルゴリズム; 応用数学; 数理工学; 可積分系

The analysis on the Toda equation and its related discrete integrable systems has been developed by using the theory of the orthogonal polynomials and the theory of Hirota's tau-function. In particular, we focus on the "non-autonomous discrete integrable systems". Then we are able to construct the theory of these systems from the point of view of the special functions. In addition, we formulate the numerical algorithms of some class of the generalized eigenvalue problems.

利用正交多项式理论和Hirota tau函数理论对Toda方程及其相关离散可积系统进行了分析。我们特别关注“非自治离散可积系统”。然后我们就能够从特殊函数的角度构建这些系统的理论。此外，我们还制定了某类广义特征值问题的数值算法。

项目成果

A difference analogue of the Davey-Stewartson system: discrete Gram-type determinant solution and Lax pair

Davey-Stewartson 系统的差分模拟：离散 Gram 型行列式解和 Lax 对

• 发表时间: 2007
• 作者: Gegenhasi; X;S. Tsujimoto
• 通讯作者: S. Tsujimoto

Integrable discrete time chains for the Frobenius-Stickelberger-Thiele polynomials

Frobenius-Stickelberger-Thiele 多项式的可积离散时间链

• 作者: V.P.Spiridonov; S.Tsujimoto; A.Zhedanov
• 通讯作者: A.Zhedanov

Integrable discrete time chains for the Frobenius-Stickelberger-Thiele polynomials

Frobenius-Stickelberger-Thiele 多项式的可积离散时间链

• 发表时间: 2007
• 作者: V. P. Spiridonov; S. Tsujimoto; A. Zhedanov
• 通讯作者: A. Zhedanov

Determinant solutions of the nonautonomous discrete Toda equation associated with the deautonomized discrete KP hierarchy

与非自治离散 KP 层次相关的非自治离散 Toda 方程的行列式解

• 作者: S. Tsujimoto

歪直交多項式のスペクトル変形

斜正交多项式的谱变换

• 发表时间: 2009
• 作者: 三木啓司; 辻本諭
• 通讯作者: 辻本諭